Inductive Reasoning Page 1 of 7. Inductive Reasoning

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1 Inductive Reasoning Page 1 of 7 Inductive Reasoning We learned that valid deductive thinking begins with at least one universal premise and leads to a conclusion that is believed to be contained in the argument s premises. Indeed, if the premises are true and the argument form is valid, the conclusion must be true. The universal statement in a syllogism allows us to move from a proposition about an entire class to a statement about some or all members of a class. We will look at arguments that move from a particular premise to a universal conclusion. Such arguments are examples of inductive reasoning. (Specific to General). Traditionally, the study of inductive logic was confined to either arguments by analogy or else methods of arriving at generalizations on the basis of a finite number of observations. A typical argument by analogy proceeds from the premise that two objects are observed to be similar with respect to a number of attributes to the conclusion that the two objects are also similar with respect to another attribute. The strength of such arguments depends on the degree to which the attributes in question are related to each other. 1 Remember that deductive reasoning begins with two or more premises and derives a conclusion that must follow from those premises. The basic form of deductive reasoning is the syllogism. Inductive reasoning begins with a set of evidence or observations about some members of a class. From this evidence or observation we draw a conclusion about all members of a class. (Specific to general). Because of this move from the particular to the general, the conclusions of good inductive reasoning likely or probably follow from the observation; the do not absolutely follow. By moving from the particular to the general, the conclusions of inductive reasoning are not logically contained in the premises. We can see this in the following inductive argument. 1 Britannica 2001 Deluxe Edition CD-ROM,

2 Inductive Reasoning Page 2 of 7 Every day I notice that the sun rises in the east and sets in the west. Though I ll be dead in one hundred years, I know that my grandchildren will also see the sun rise in the east and set in the west. In all likelihood the grandchildren will make the observations predicted. However,, it is not necessarily the case. It could be, although it is unlikely, that the earth will encounter some cosmic matter or force that unsettles its rotation such that the sun rises in the north and sets in the south. The only way we will know for sure is to wait until the grandchildren observe the sun. In inductive reasoning the premises of the argument consist of the evidence or observations from which we derive our conclusion. As in deductive arguments, these premises can be challenged. For example, if we see three black crows and conclude that all crows are black, someone could say, Well, you saw them far away, didn t you? Don t you know that colors disappear with distance, and even if they were red they would have looked black to you? Thus the observation is challenged. Science, which relies heavily on the inductive method, often faces challenges this way, as when someone points out that the results of a particular experiment are flawed because of poor experimental design. Often deductive arguments contain premises that are inductively derived. Consider the following: If the stock market crashes, then the suicide rate will rise. The stock marked crashed. Therefore, the suicide rate will rise. In this hypothetical syllogism, the first premise is really a conclusion of inductive reasoning: Whenever the stock market crashed in the past, the suicide rate went up. Therefore, if the stock market crashes again, the suicide rate will go up. Many of the syllogisms we looked at contain premises that are based on inductive reasoning. And as

3 Inductive Reasoning Page 3 of 7 we learned, these inductive premises can often be challenged, thereby weakening the deductive argument. Inductive reasoning can also be challenged by finding evidence contrary to the conclusion. Let us go back to the evidence in our example with the black birds: I saw three crows today and all them were black. The conclusion is that therefore all crows are black. The conclusion of this argument would be refuted instantly if someone found a red or blue crow. Thus, the conclusions of inductive arguments, even with true premises, are always open to the possibility, however unlikely, that they are false, for they are statements of probability, not certainty. In contrast, the conclusion of a deductive argument cannot be false, given true premises and valid syllogistic form. Consider the following inductive argument: Because no other planet in the solar system has any signs of even the lowest form of life, we must conclude that we are the only intelligent creatures in the universe. Here the argument went from the particular no life on any other planets in our solar system to the general no life on any other planets in any solar system. This conclusion can be disputed in several ways: we can attack the methods that have been used so far to search for life, that is, attack the observation; we can argue that the number of planets that we have observed is too small to justify a generalization to all planets; or we can actually discover life on another planet, a possibility that is not foreclosed by the inductive conclusion. Discovering life on another planet would definitely refute the conclusion above. However, one commonly attacks the inductive argument with another inductive argument, that is, with evidence or observation that suggests a contrary conclusion. For example, astronomers have discovered planets revolving around nearby stars and can argue from this evidence that our planetary system is not unusual, that many or most stars have planets. Therefore, considering the billions of stars in each galaxy and the billions of galaxies in the universe, it is highly unlikely that life exists only on earth. This evidence of other planetary systems in our galaxy does not refute the previous conclusion that there is no life in the universe except on earth, but is certainly weakens it.

4 Inductive Reasoning Page 4 of 7 Given induction s apparent uncertainty, is there any such thing as a sound inductive argument? We have seen that sound deductive arguments are valid arguments with true premises and therefore conclusively true conclusions. Some philosophers, such as the skeptic David Hume, argue that there are no absolutely sound inductive arguments that all inductive arguments fall short of yielding conclusions as certain as those in sound deductive arguments but there are good practical inductive arguments. If the argument is based on repeated, accurate observations, and as we will see, if the analogies used are based on strong significant similarities rather than on weak ones, then the induction may be, practically speaking, rather solid. Such strong inductive arguments can be referred to as sound as long as we understand that their conclusions are not absolute, as they are in sound deductive arguments. We use sound inductions every day; indeed, it would be difficult to live without them. Here are some examples: 1. Driving to work after a fresh snow we notice several cars in the ditch. Just after this observation we see a car ahead of us spin out of control. We conclude from these observations that the roads in our area are slippery because of the new fallen snow. We slow down and drive very carefully the rest of the way to work. 2. We let our cat out of our house and notice that it runs behind a neighbor s garage. We let our cat out the next day and it runs there again. And on the third day our cat again runs behind our neighbor s garage. We conclude from these observations that our cat will run behind the garage upon being let out. We decide to talk to our neighbors to see if they mind if our cat roams on their property. 3. We are dropped off from work and wave our friend on before we open the door. We have the keys to the house and we know that we will be able to get

5 Inductive Reasoning Page 5 of 7 in. We know this because our keys have worked in our lock hundreds of times before. Conclusions of good inductive reasoning are highly probable, but never certain. In the above examples, the conclusions could have been wrong. Consider these possibilities: 1. The roads are only slippery along this stretch of road because a water main broke and the water froze under the snow. All other roads were just fine. 2. The cat went behind the neighbor s garage because the neighbor had some garbage from Thanksgiving Day back there, and the cat had a fancy for turkey. After the garbage was collected the cat was no longer interested. 3. We waved our friends on knowing that we had our keys and could get in. Unfortunately, the keys didn t work this time because the lock was broken. Thinking Activity: Distinguishing Between Inductive and Deductive Arguments Analyze the seven statements below for the kind of reasoning used. Place an I in front of the inductive arguments and D in front of deductive ones. Be careful that you do not confuse premises derived through induction with the inductive form of argument. 1. Anything that questions the fact of its own existence must exist. I question the fact of my own existence. Therefore, I must exist. 2. Every person who questions the fact of their own existence is depressed. Mary has recently been questioning the fact of her own existence. Therefore, Mary must be depressed. 3. If a woman gets married, she will regret it. Sharon is getting married soon. Therefore, Sharon will eventually regret it.

6 Inductive Reasoning Page 6 of 7 4. My friend is a very intellectual person but also quite neurotic. So, I think intelligent people in general, perhaps because they are so overdeveloped in their intelligence, must be underdeveloped elsewhere, leaving them with somewhat disturbed personalities. 5. I have never won a thing in my life, and I never will. It is not in my karma. 6. No human being lies all the time. Therefore, Mary does not, as you suggest, lie all the time maybe a lot but not all the time. 7. No species on this planet has survived for more than 100 million years. The human race will be no exception. Thinking Activity: Consider Past Errors List examples of erroneous inductive reasoning that you have used in the past. Consider reasoning that you do at work, at hove, and in your relationships. For each example, identify why your conclusions were wrong. Were they based on too few observations, or were the errors due to some very unusual circumstances? 1. Example: Reason for Error: 2. Example: Reason for Error: 3. Example: Reason for Error:

7 Inductive Reasoning Page 7 of 7 Reference: Thinking by Kirby and Goodpaster, 1999 by Prentice-Hall, Inc. Used with written permission.

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Section 1.5 Methods of Proof 1.5.1 1.5 METHODS OF PROOF Some forms of argument ( valid ) never lead from correct statements to an incorrect. Some other forms of argument ( fallacies ) can lead from true